Hom-algebras and homology

Abstract

Classes of $G$-Hom-associative algebras are constructed as deformations of $G$-associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as deformations of associative and Lie algebras, respectively, along algebra endomorphisms. Chevalley-Eilenberg type homology for Hom-Lie algebras are also constructed.

arXiv comment11 pages. Theorem 2.4 now covers G-associative algebras. To appear in Journal of Lie Theory

References in corpus (4)

• Deformations of Lie Algebras using $\sigma$-derivations
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Module Hom-algebras
• Hom-Algebras and Hom-Coalgebras

Cited by in corpus (96)

• Representations of hom-Lie algebras
• Hom-bialgebras and comodule Hom-algebras
• Hom-quantum groups I: quasi-triangular Hom-bialgebras
• BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
• Hom-Lie 2-algebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Module Hom-algebras
• Hom-Lie algebroids
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• On unitality conditions for Hom-associative algebras
• Hom-quantum groups III: Representations and module Hom-algebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
• Cyclic homology for Hom-associative algebras
• Hom-alternative algebras and Hom-Jordan algebras
• Non-commutative Hom-Poisson algebras
• On Hom type algebras
• Hom-Algebras and Hom-Coalgebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras
• On Hom-Gerstenhaber algebras and Hom-Lie algebroids
• Non-associative algebraic structures: classification and structure
• Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras
• On hom-algebras with surjective twisting
• Cohomology and 1-parameter formal deformations of Hom-Lie triple systems
• Quadratic color Hom-Lie algebras
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
• A twisted generalization of Lie-Yamaguti algebras
• A Hom-associative analogue of n-ary Hom-Nambu algebras
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• On the hom-associative Weyl algebras
• Generalized Derivations and Rota-Baxter Operators of $n$-ary Hom-Nambu Superalgebras
• Constructions and Cohomology of color Hom-Lie algebras
• Hom-power associative algebras
• Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras
• Hom-algebras via PROPs
• Hom-Lie superalgebra structures on finite-dimensional simple Lie superalgebras
• Some characterizations of Hom-Leibniz algebras
• A twisted generalization of Novikov-Poisson algebras
• Right Hom-alternative algebras
• Hom-Alternative, Hom-Malcev and Hom-Jordan superalgebras
• Quadratic $n$-ary Hom-Nambu algebras
• Hopf-Galois extensions for monoidal Hom-Hopf algebras
• Split Regular $Hom$-Leibniz Color $3$-Algebras
• Non-degenerate Killing forms on Hom-Lie superalgebras
• Relative Hom-Hopf modules and total integrals
• Bimodules over Hom-Jordan and Hom-alternative algebras
• Construtions and bimodules of BiHom-alternative and BiHom-Jordan algebras
• A complement on representations of Hom-Lie algebras
• Hom-Lie-Yamaguti structures on Hom-Leibniz algebras
• On split regular Hom-Leibniz-Rinehart algebras
• A non-abelian Hom-Leibniz tensor product and applications
• Crossed modules for Hom-Lie antialgebras
• Extensions of hom-Lie color algebras
• On the cohomology and extensions of $n$-ary multiplicative Hom-Nambu-Lie superalgebras
• Hom-Akivis algebras
• Hom-entwining structures and Hom-Hopf-type modules
• On universal central extensions of Hom_Leibniz algebras
• Supercommutator algebras of right (Hom-)alternative superalgebras
• Covariant Bimodules Over Monoidal Hom-Hopf Algebras
• Cohomology and Versal Deformations of Hom-Leibniz algebras
• On the structure theorem and the Maschke type theorem of Doi Hom-Hopf modules
• Structures and bimodules of simple Hom-alternative algebras
• A non-abelian tensor product of Hom-Lie algebras
• The hom-associative Weyl algebras in prime characteristic
• Ado theorem for nilpotent Hom-Lie algebras
• Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras
• On 3-Hom-Lie-Rinehart algebras
• Generalized derivations of Hom-Jordan algebras
• Hom-Lie-Hopf algebras
• Constructions and generalised derivations of multiplicative n-BiHom-Lie color algebras
• A non-abelian exterior product of Hom-Leibniz algebras
• On the capablility of Hom-Lie algebras
• Covariant Differential Calculus Over Monoidal Hom-Hopf Algebras
• Structure and classification of Hom-associative algebras
• Deforming algebras with anti-involution via twisted associativity
• Hom-pre-Malcev and Hom-M-Dendriform algebras
• The exterior product and homology of Hom-Lie algebras
• Z-graded Hom-Lie Superalgebras
• Matching Hom-Setting of Rota-Baxter algebras, dendriform algebras and pre-Lie algebras
• Universal central extensions of Hom-Lie antialgebras
• Classification of 3-Dimensional BiHom-Associative and BiHom-Bialgebras
• Equivalent description of Hom-Lie algebroids
• Hom-coassociative ternary coalgebras and infinitesimal bialgebras
• Enveloping algebras of color hom-Lie algebras
• Restricted hom-Lie algebras
• Super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras
• On hom-Lie algebras
• On the deformations and derivations of $n$-ary multiplicative Hom-Nambu-Lie superalgebras
• Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras
• A new approach to hom-Lie bialgebras
• A Maschke type theorem for relative Hom-Hopf modules
• Braided monoidal categories and Doi Hopf modules for monoidal Hom-Hopf algebras
• Constructing New Braided $T$-Categories via Weak Monoidal Hom-Hopf Algebras